Strollers generally may be extended to a usage state and collapsed to a folding state. When folding the stroller from the usage state to the folding state, the baby sitting in the stroller has to be taken out before the folding structure may be operated. In the event that the baby is still not capable of standing alone or walking, the user often has to hold the baby with one hand and operate the folding structure with the other hand, which is inconvenient. To remedy this problem, strollers that are foldable single-handedly have been developed. References can be found in U.S. Pat. No. 6,068,284 and R.O.C. publication No. 262689. In those structures, the frame collapses to the folding state after the operating structure is released. In order to prevent improper operations that result in accidental collapsing of the frame and cause injury to the baby sitting in the stroller, the conventional single-handed operation structures usually have a safety lock. The safety lock has to be released before the single-handed operation structure is actuated to release the frame. However, the commonly used safety locks can be released by operating in only one direction, and they are mostly designed to be operated by the thumb. When users have to hold the baby or goods with one hand and release the safety lock with the other hand, it is awkward and inconvenient. Sometimes users have to switch hands for holding the baby or goods, and use the other hand to release the unidirectional safety lock. This is a cumbersome operation.